Math, philosophy: transitivity, part 0

Tutoring math, you encounter ideas that manifest in real life. The tutor mentions transitivity.

Where and when I took grade 10 math, part of the curriculum was geometric proofs. It was completely different from the rest of the course: no calculation was involved.

I entered that class at a deficit because I’d come from a much less robust grade 9 curriculum (from another location). Since my grade 9 mark was high I took honours grade 10 math at this big-city school. Within a week I realized that my cohort, who’d taken honours math the previous grades, were far ahead of me. Yet I had faith I’d manage; school’d never given me trouble before.

For some reason, the geometric proofs challenged the class in a way the other topics didn’t. The teacher observed one day: “When you people need to calculate something, you’re good to go; you’re not so strong with the proofs.” BTW: I noticed his observation as a general rule in subsequent math courses.

As usual, I wasn’t “like the others”: I lacked their strong calculation background. However, the geometric proofs didn’t flap me the way they did some people. I guess to me, everything was hard that year, so the geometric proofs weren’t harder than anything else.

A true math lover, the grade 10 honours math teacher loved those proofs. (Many of the kids picked up on this, so went the other way.)

One idea the teacher loved was transitivity: if A=B and B=C, then A=C. While obvious enough, it was the duct tape of many proofs that he did on the board, and that we did in assignments and tests.

At that school, you took the same courses all year. It took me from September until May to “catch up” with the class. The geometric proofs, and that teacher’s love of them, showed me the clouds would part.

BTW: transitivity isn’t just mathematical. I’ll be following up:)

Source:

cut-the-knot.org